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3 years ago

Is the sequence geometric or arithmetic?6,18,54...

Mathematics

1 answer:

serious [3.7K]3 years ago

4 0

Answer:

geometric sequence

Step-by-step explanation:

The consecutive terms of an arithmetic sequence have a common difference d between them.

18 - 6 = 12

54 - 18 = 36

There is no common difference, thus not arithmetic

The consecutive terms of a geometric sequence have a common ratio r between them.

18 ÷ 6 = 3

54 ÷ 18 = 3

There is a common ratio, thus sequence is geometric

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$\frac{r + 5}{r^{2}+5r - 14 }$ ÷ $\frac{r^{2}+4r - 21 }{r - 2}$

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3 years ago

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MA_775_DIABLO [31]

Answer:

The answer is below

Step-by-step explanation:

a) The patio is in the form of a rectangle. The patio has a width of (x - 10) ft. Therefore given that the area of the patio is x² + 10x - 200, hence:

$Area=length*breadth\\\\x^2+10x-200=length*(x -10)\\\\x^2+20x-10x-200=length*(x -10)\\\\x(x+20)-10(x+20)=length*(x -10)\\\\(x-10)(x+20)=length*(x -10)\\\\length=x +20$

b) Area of original house = length of house * breadth of house

The length of house = length of patio = x + 20; breadth of house = x + 10; therefore:

Area of original house = (x + 20)(x + 10) = x² + 10x + 20x + 200

Area of original house = x² + 30x + 200

c) If the width is extended, hence:

$Area=length*breadth\\\\x^2+12x-160=(x+20)*width\\\\x^2+20x-8x-160=(x+20)*width\\\\x(x+20)-8(x+20)=(x+20)*width\\\\(x-8)(x+20)=(x+20)*width\\\\width=x-8\\\\Extended \ width=(x-8)-(x-10)\\\\Extended \ width=2\ feet$

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3 years ago